Advertisements
Advertisements
प्रश्न
\[\int2 x^3 e^{x^2} dx\]
बेरीज
Advertisements
उत्तर
\[\int2 x^3 \cdot e^{x^2} dx\]
\[ = \int x^2 \cdot \left( e^{x^2} \right) \cdot \text{ 2x dx }\]
` \text{ Let } x^2" = t `
\[ \Rightarrow \text{ 2x dx } = dt\]
\[ = \int t_I \cdot {e_{II}}^t dt\]
\[ = t \cdot e^t - \int1 \cdot e^t dt\]
\[ = \text{ t e}^t - e^t + C\]
\[ = \text{ x}^2 \text{ e}^{x^2} - e^{x^2} + C\]
\[ = e^{x^2} \left( x^2 - 1 \right) + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left\{ x^2 + e^{\log x}+ \left( \frac{e}{2} \right)^x \right\} dx\]
\[\int \left( a \tan x + b \cot x \right)^2 dx\]
\[\int\frac{x^3 - 3 x^2 + 5x - 7 + x^2 a^x}{2 x^2} dx\]
\[\int\frac{x^2 + x + 5}{3x + 2} dx\]
\[\int \text{sin}^2 \left( 2x + 5 \right) \text{dx}\]
\[\int\frac{1 - \sin x}{x + \cos x} dx\]
` ∫ tan^3 x sec^2 x dx `
` ∫ \sqrt{tan x} sec^4 x dx `
\[\int\frac{1}{\sin x \cos^3 x} dx\]
\[\int\frac{1}{\sqrt{1 + 4 x^2}} dx\]
\[\int\frac{1}{\sqrt{16 - 6x - x^2}} dx\]
\[\int\frac{x}{\sqrt{4 - x^4}} dx\]
\[\int\frac{x + 2}{2 x^2 + 6x + 5}\text{ dx }\]
\[\int\frac{x + 7}{3 x^2 + 25x + 28}\text{ dx}\]
\[\int\frac{6x - 5}{\sqrt{3 x^2 - 5x + 1}} \text{ dx }\]
\[\int\frac{x + 2}{\sqrt{x^2 + 2x - 1}} \text{ dx }\]
\[\int\frac{x - 1}{\sqrt{x^2 + 1}} \text{ dx }\]
\[\int\sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int\frac{1}{\cos x \left( \sin x + 2 \cos x \right)} dx\]
\[\int\frac{2 \sin x + 3 \cos x}{3 \sin x + 4 \cos x} dx\]
\[\int\frac{8 \cot x + 1}{3 \cot x + 2} \text{ dx }\]
\[\int x e^{2x} \text{ dx }\]
\[\int x^2 e^{- x} \text{ dx }\]
\[\int x\ {cosec}^2 \text{ x }\ \text{ dx }\]
\[\int e^x \frac{1 + x}{\left( 2 + x \right)^2} \text{ dx }\]
\[\int\frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x/2} \text{ dx }\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x - 2 \right) \left( x - 3 \right)} dx\]
\[\int\frac{3x + 5}{x^3 - x^2 - x + 1} dx\]
\[\int\frac{\cos x}{\left( 1 - \sin x \right)^3 \left( 2 + \sin x \right)} dx\]
\[\int\frac{x^3}{x + 1}dx\] is equal to
\[\int \sin^4 2x\ dx\]
\[\int\frac{\sin x - \cos x}{\sqrt{\sin 2x}} \text{ dx }\]
\[\int\frac{\sin x}{\cos 2x} \text{ dx }\]
\[\int\frac{x^2}{\left( x - 1 \right)^3} dx\]
\[\int\frac{1}{\sin x + \sin 2x} \text{ dx }\]
\[\int {cosec}^4 2x\ dx\]
\[\int\sqrt{3 x^2 + 4x + 1}\text{ dx }\]
\[\int\frac{\log x}{x^3} \text{ dx }\]
